The rules for the number built-ins (Feel.Analysis.Images, D-161): the type of the result of a call of abs, ceiling,
decimal, even, exp, floor, log, modulo, odd, round down, round half down, round half up, round up
and sqrt, from the types of the arguments.
| Function | The numbers it gives | null for |
|---|
| abs(x) | |x|, exactly (the same for a duration) | nothing |
| floor, ceiling, round * (x, scale), decimal(x, scale) | the multiples of 10^-scale from the result at the lower end to the one at the upper, exactly (Rounding) | a scale that is not in -6111..6176 |
| modulo(x, y) | the residues, exactly for a divisor that is one number, a hull for many (Modulo) | a zero divisor, and a result of more than 34 digits |
| sqrt(x) | the run's roots at the ends (Real) | a negative x |
| log(x) | the run's logarithms at the ends | x <= 0 |
| exp(x) | the run's results at the ends, or from the smallest number if the result can be too small | an x whose result is past the range or too small to write (found with the run) |
| even(x), odd(x) | a boolean for the whole numbers of the set, exactly | a number with a fraction |
What the type of an argument is for. The run gives null for a null argument, and for one of a kind that the function
does not take (with an error); abs takes the two kinds of duration as well. A list of one element is that element
(section 10.3.2.9.4): the elements of a list type are read as the argument, and the list gives null for any other length,
so a type of lists has Null. An argument of a type that may be anything (Any, a named type) is every number and, for
abs, every duration, and may give null. So Null is in the type of the result when an argument may be null or of
another kind, or when a number of the argument is one the function has no result for.
The sets are hulls where the result is not every number between its ends: floor(x) for x in [0.5..3.7] is the whole
numbers 0, 1, 2, 3, and the type says [0..3]. A hull holds every number the run gives, which is what a type has to do;
the granularity (that the result is a multiple of a step) is step D of D-161.